In many applications it is necessary to calibrate a device to a known reference. For example, color characterization could be performed using an off-line spectrophotometer. The off-line device would measure patches on a device to be color corrected and an algorithm was executed that produced a color correction for the device. However, this process was highly resource intensive and required the operator to print a test target, measure it off-line and load the calculated correction on the device.
In order to simplify the process an in-line spectrophotometer (ILS) was inserted into the printer path for some machines. In order to maintain the color accuracy of the color profiling system the ILS needed to be modified to emulate the reference device that it is supplanting. This calibration was accomplished using a 31×31 conversion matrix that estimates the 31 spectral values of the reference device from the spectral measurements of the machine device.
One technique for generating the matrix is an empirical solution that uses a pseudo-inverse technique. Unfortunately, the inversion technique does not work well for the ILS characterization problem. The matrix for the ILS problem is ill-conditioned and the inverse is not stable. Adding a small amount of noise to either the ILS spectral data or the reference device data will result in drastically different values for the matrix. The cause of the numerical instability is that all colors are created through weighted combinations of cyan, magenta, yellow and black (CMYK), so in reality there are only about 7 degrees of freedom in determining the varying spectral of the ILS and reference device. In order to get more degrees of freedom more unique inks are needed. Unfortunately, it is not possible to circumvent this limitation by increasing the number of patches measured as they are all constrained to vary in the seven degrees of freedom.